Method for testing transducer horn assembly used in debubbling by monitoring operating frequency via impedance trace

ABSTRACT

A method and apparatus for evaluating the end cap round transducer horn assemblies used in debubbling operations wherein the ECR THA can be evaluated off-line at both high and low power and on-line by making electrical measurements on the ECR THA. The electrical measurements are used to characterize the physical condition of the piezoelectric ceramics of the THA. A test box is employed to practice the method. The test box is connected between the THA and a signal analyzer. Power is supplied to the THA and the electrical signals across the THA are sampled. The sampled electrical signals are transmitted to the signal analyzer while maintaining the amplitude and phase relationship thereof. The sampled electrical signals are used to generate an impedance trace for the particular THA. That impedance trace is compared to a model impedance trace. In such manner, it can be determined whether the ECR THA is operational. Further, if the ECR THA is in working condition, the impedance trace can be used to determine how efficiently it is operating. This allows for an ultimate determination to be made of how well a particular ECR THA is functioning.

CROSS REFERENCE TO RELATED APPLICATION

This application is a division of U.S. application Ser. No. 09/239,184,filed Jan. 28, 1999 which is a continuation of U.S. application Ser. No.08/740,585, filed Oct. 31, 1996 now abandoned.

FIELD OF THE INVENTION

The present invention relates generally to transducer horn assemblydebubbling devices and, more particularly, to methods and apparatus formeasuring the electrical and mechanical characteristics of a transducerhorn assembly and for determining the effectiveness of the transducerhorn assembly in debubbling operations.

BACKGROUND OF THE INVENTION

There are a variety of emulsions, suspensions, pastes and high viscosityliquids used in the manufacture or which become part of the variety ofproducts in the chemical, pharmaceutical, food products, andphotographic industries. These emulsions, suspensions, pastes and highviscosity liquids often contain air or gases which are dissolved thereinor are present in the form of small bubbles. Often this air or gas,particularly in the case of entrained bubbles, is detrimental to thefinal product being produced. For example, in the case of photographicemulsions, the gas bubbles greatly impair the quality of the films orphotographic papers produced with these emulsions because the bubblesdisturb the evenness of volumetric flow of the emulsion as it is appliedby the coating devices. This gives rise to the formation of streaks andspots making the photographic materials unusable.

An apparatus which is typically used in the photographic industry fordebubbling photographic emulsions is an end cap round ultrasonic bubbleeliminator, typically referred to as an ECR. The ECR includes atransducer horn assembly (hereinafter referred to as a "THA") which isan electromechanical device which converts electrical vibration tomechanical vibration. One particular ECR with its component THA istaught in U.S. Pat. No. 5,373,212 to Beau. In the operation of an ECR,an alternating voltage is applied to the ceramic disk of the THA which,as a result, generates mechanical vibration. This mechanical vibrationresults in the debubbling of the photographic emulsions flowing throughthe ECR.

The effectiveness and efficiency of an ECR THA in the performance ofdebubbling operations can be critical to whether or not an acceptablefinal product is produced. In the past there has been no practicalmethod for testing the effectiveness and efficiency of an ECR THA and,therefore, an ECR THA which was no longer performing adequately was notreplaced or repaired until it had resulted in the production of productwhich was out of specification or otherwise not useful. As a result, ameans of testing the effectiveness and efficiency of the ECR THA wasneeded. Preferably, testing of the ECR THA could be performed on-line.

SUMMARY OF THE INVENTION

It is, therefore, an object of the present invention to provide a methodand apparatus for testing ECR THA's to determine and to predict thedebubbling efficiency of the ECR itself.

A further object of the present invention is to provide a method andapparatus for testing an ECR THA's which can be performed at either lowor high power with the ECR off-line.

Still another object of the present invention is to provide a method andapparatus for testing ECR which can be performed with the ECR operatingon-line.

Briefly stated, these and numerous other features, objects andadvantages of the present invention will become readily apparent upon areading of the detailed description, claims and drawings set forthherein. These features, objects and advantages are accomplished bymaking electrical measurements on the ECR THA and using thosemeasurements to characterize the physical condition of the piezoelectricceramics of the THA. In order to make electrical measurements on an ECRhorn, it is necessary to measure the voltage and current drive signals.Since the ECR operates at high frequencies, nominally 40 kHz, anaccurate alternating current measurement is required. The measurementmust have a band width sufficient to maintain the fidelity of thesignals and it must preserve the phase relationship between the voltageand current signals. A test box is connected between the ECR and asignal analyzer. The test box contains an electrical circuit whichincludes a current transformer in the supply leg of the drive signalbeing supplied to the horn, and a high impedance voltage divider betweenthe supply and return legs. The current transformer provides an outputvoltage that is proportional to the current in the supply leg. Thevoltage divider provides a voltage signal that is 1/100th of the drivevoltage. Capacitors are added to the circuit to compensate for straycapacitance in the voltage divider that can lead to unwanted phaseshifts between the output of the voltage divider and the signal suppliedto the current transformer. By making these measurements, an impedancetrace can be generated for the horn. This impedance trace is compared toa model impedance trace. The model impedance trace has been developedfor the purpose of understanding and predicting the performance of ECRTHAs. Impedance measurements made directly on the ECR THAs have beenused to confirm the model. Through the comparison of the impedance tracemade for a particular ECR with the model, it can be determined whetherthe ECR is operational, that is, whether it is in good condition ordamaged. Further, if the ECR is in working condition, the impedancetrace can be used to determine how efficiently the ECR is operating. Inthis manner, an ultimate determination of how well a particular ECR isfunctioning as a debubbler can be made.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of the ECR test box of the present inventionconnected to a signal analyzer and to an ECR THA for testing the THA inan off-line, low power configuration.

FIG. 2 is a schematic of the ECR test box of the present inventionconnected to a signal analyzer and to an ECR THA for testing the THA inan off-line, high power configuration.

FIG. 3 is a schematic of the ECR test box of the present inventionconnected to a signal analyzer, an ECR generator and ECR THA for testingthe ECR THA on-line.

FIG. 4 is a circuit schematic for the electrical circuit within the ECRtest box of the present invention.

FIG. 5 depicts the magnitude of an impedance trace for a good THA testedunder the set-up depicted in either FIG. 1 or FIG. 2.

FIG. 6 depicts the phase of an impedance trace for a good THA testedunder the set-up depicted in either FIG. 1 or FIG. 2.

FIG. 7 depicts the magnitude of an impedance trace for a bad THA testedwith the set-up depicted in either FIG. 1 or FIG. 2.

FIG. 8 depicts the phase of an impedance trace for a good THA testedunder the set-up depicted in either FIG. 1 or FIG. 2.

FIG. 9 shows an on-line measurement of current as a function offrequency of an ECR THA made with the test set-up depicted in FIG. 3.

FIG. 10 shows an on-line measurement of power as a function of frequencyof an ECR THA made with the test set-up depicted in FIG. 3.

FIG. 11 shows an on-line measurement of voltage as a function offrequency of an ECR THA made with the test set-up depicted in FIG. 3.

FIG. 12 shows an on-line measurement of real power as a function offrequency of an ECR THA made with the test set-up depicted in FIG. 3.

FIG. 13 shows an on-line measurement of volts per amp as a function offrequency of an ECR THA made with the test set-up depicted in FIG. 3.

FIG. 14 is an equivalent circuit schematic for a piezoelectrictransducer and its use as a source of ultrasonic energy where both theelectrical and mechanical portions of the transducer are represented byelectrical equivalents.

FIG. 15 is an electrical circuit diagram modeling the electrical andmechanical sides of a transducer.

FIG. 16 is an impedance trace for a new ECR THA.

FIG. 17 is the theoretical response curve for the equivalent circuitdepicted in FIG. 15.

FIG. 18 is the equivalent circuit diagram for a transducer under liquidload modified to include losses within the horn (R_(loss)), mechanicalradiation (R_(load)), and dielectric loss (R_(d)).

FIG. 19 is the equivalent circuit diagram for a transducer at seriesresonance under liquid load modified to include losses within the horn(R_(loss)) mechanical radiation (R_(load)) and dielectric loss (R_(d)).

FIG. 20 is a graph plotting ECR THA efficiency versus impedance atseries resonance with an air load.

FIG. 21 is an impedance trace showing the model response for impedanceat series resonance of 29 ohms and a static capacitance of 2.5 nF whichare characteristic of an ECR THA under air load with six feet of coaxialcabling.

FIG. 22 is an impedance trace showing the model response for impedanceat series resonance of 150 ohms and a static capacitance of 2.5 nF whichare characteristic of an ECR THA under water load with six feet ofcoaxial cabling.

FIG. 23 is an impedance trace showing the model response for impedanceat series resonance of 150 ohms and a static capacitance of 9.1 nF whichare characteristic of an ECR THA under air load with 300 feet of coaxialcabling.

FIG. 24 is a graph plotting maximum flow rate through the ECR versuspredicted THA efficiency.

DETAILED DESCRIPTION OF THE INVENTION

Turning first to FIG. 1, there is shown a schematic for using the ECRtest box 10 of the present invention in an off-line, low powerconfiguration. The ECR test box 10 is connected both to a signalanalyzer 12 and an ECR 14 and to the THA 32 which is part of the ECR 14.The ECR test box 10 includes a supply input terminal 16, an outputterminal 18, a current output terminal 20, and a voltage divider outputterminal 22.

The signal analyzer 12, which may be any suitable signal analyzer suchas an HP3562A or HP 3567A as manufactured by Hewlett-Packard Corporationof Santa Clara, Calif., is configured to run a swept sine scan in apredetermined frequency range. As depicted in the drawings, the signalanalyzer 12 includes a source connector terminal 24, a first channelconnector 26, and a second channel connector 28. The source connectorterminal 24 is connected by means of conductor 30 to the input supplyterminal 16. The first channel connector 26 is connected to the currentoutput terminal 20 by means of conductor 31. The second channelconnector 28 also connects to input supply terminal 16 by means ofconductor 30. The output terminal 18 is connected to the THA 32 of theECR 14.

Turning next to FIG. 2, there is shown the same ECR test box 10 of thepresent invention with appropriate connections for generating a highpower impedance trace on a THA 32 with the THA 32 off-line. This highpower configuration can be used for potentials up to 800 volts. In thishigh power, off-line configuration, a power amplifier 34 is necessary.The power amplifier is connected between the source connector terminal24 and the input supply terminal 16 by conductors 33 and 35,respectively. A suitable power amplifier for use in this configurationis a Krohn-Hite 7500 as manufactured by Krohn-Hite Corp. of Avon, Mass.In this high power configuration, voltage divider output terminal 22 isconnected to the second channel connector 28 by means of conductor 36.Those skilled in the art will recognize that operation of an ECR at highpower without a liquid in the ECR can result in damage to the THA. Thus,when using the ECR test box 10 in accordance with FIG. 2, an appropriateliquid level should be maintained within the ECR.

Looking next at FIG. 3, there is shown a schematic of the ECR test box10 of the present invention with the appropriate connections in order togenerate frequency response curves for an ECR 14 on-line. In thisinstance, an ECR generator 38 is connected directly to the input supplyterminal 16 of the test box 10 by means of a conductor 40. A suitableECR generator for use in this configuration is a Wave Energy System 4002as manufactured by Wave Energy Systems of Newtown, Pa. In thisconfiguration, because the signal analyzer 12 is not being used tosupply power to the THA 32, the source connector terminal 24 of thesignal analyzer 12 is left unconnected.

Turning next to FIG. 4, there is shown a circuit schematic for thecircuit within ECR test box 10. The circuit within ECR test box 10includes a current transformer 42 in the supply leg of the drive signalbeing applied to the THA 32. The circuit also includes a high impedancevoltage divider 44 (that portion of the circuit contained within thedotted line box) between the supply and return legs to and from theultrasonic horn of the THA 32. The current transformer 42 provides anoutput voltage that is proportional to the current in the supply leg.For example, the output of the current transformer 42 is 10 volts/ampand the voltage divider provides a voltage signal that is 1/100th of thedrive voltage or 0.01 volts/volt. The high impedance voltage divider 44includes a first resistor 46, a second resistor 48 and a third resistor50 which are in series. The high impedance voltage divider 44 alsoincludes a first capacitor 52, a second capacitor 54 and the thirdcapacitor 56. First capacitor 52 is in parallel with first resistor 46.Second and third capacitors 54, 56 are parallel to one another andparallel with second and third resistors 48, 50. First, second and thirdcapacitors 52, 54, 56 are added to compensate for stray capacitance inthe voltage divider 44 that can lead to unwanted phase shifts betweenthe output of the voltage divider 44 and the signal supplied by thecurrent transformer 42. The capacitors 52, 54, 56 allow a user to adjustthe circuit to compensate for such stray capacitance. Under theseconditions, the test box offers 10 pf to 20 pf of shunt capacitance thatresults from the internal wiring of the test box 10. There is nocompensation for this capacitance. This test box capacitance is lessthan the capacitance of one foot of standard coaxial cable, which forRG58C/U is 30.8 pf/ft³. Since the measured static capacitance of an ECRhorn is approximately 4000 pf, the test box capacitance can beneglected.

When the ECR test box 10 of the present invention is used in highvoltage applications (see FIGS. 2 and 3), both the voltage divideroutput 22 and the current output 20 are used. When the test box 10 isused in a low voltage application (see FIG. 1), only the current output20 is used. In the low voltage application, the voltage signal comesdirectly from the source output 24 of the dynamic signal analyzer 12.The dynamic signal analyzer 12 must have a band width of at least 100kHz and should be capable of swept sine output. Further, the dynamicsignal analyzer 12 should have at least two input channels and theanalysis capability to ratio the input channels and provide a frequencydependent impedance trace in the form of magnitude and phase.

The method and test box 10 of the present invention provide for thegeneration of an impedance trace and response curves for an ECR horn. Assuggested above, impedance traces describe the electromechanicalcharacteristics of ECR horns. These traces can be related to theelectrical equivalent circuit model of the horn. The shape of theimpedance trace can be related to the physical condition of the horn.

Looking next at FIGS. 5 and 6, there is shown an impedance trace for agood horn tested under the set-up depicted in either FIG. 1 or FIG. 2.The low point 60 of the impedance trace in FIG. 5 is indicative of theseries resonance point, that being at slightly more than 40 kHz. Thehigh point 62 of the impedance trace set forth in FIG. 5 is indicativeof the parallel resonance point. The impedance traces depicted in FIGS.7 and 8 are indicative of a bad horn. Again, the impedance trace as setforth in FIGS. 7 and 8 were generated with a horn tested with either theset-up of FIG. 1 or FIG. 2.

FIGS. 9 through 14 show voltage, current, power (watts), complex power(volts-amps), and power factor as a function of frequency during anon-line measurement of an ECR horn made with the test set-up shown inFIG. 3. These figures are the measured frequency spectra of the primaryelectrical parameters, voltage and current collected simultaneouslyduring on-line operation of the ECR, and additional electrical spectracalculated from the measured spectra. FIG. 9 shows that the ECR isdrawing 102.679 mA at its present operating frequency of 41.522 kHz.FIG. 11 shows that its operating voltage is 201.165 Vrms (the frequencyis the same as it should be). FIGS. 9 and 11 also show a series ofsidebands around the main frequency peak. The sidebands are a result ofthe operating characteristics of the ECR generator and are alwayspresent in the various ECR generators we use.

FIGS. 10, 12, and 13 are spectra calculated from the voltage and currentspectra. Spectra in FIGS. 10 and 12 are power spectra resulting from theproduct of V and I (FIG. 11 times FIG. 9). FIG. 10 is the product of themagnitude of V*I. FIG. 12 is the real power which includes thecontribution of the phase angle between V and I. P=V*I*cos(Θ)) where Θis the phase angle. The analyzer makes this calculation by taking thereal part of the V*I product shown in FIG. 10. Comparing the two powermeasurements indicates how well the ECR generator is tuned. FIG. 13 isthe ratio of the volts and amps, V/I. You will note that this is thesame definition as impedance and indeed FIG. 13 has the same shape asthe previously described impedance traces, except more noisy. Bycomparing one of the primary spectra (i.e., voltage) with the V/I traceof FIG. 13, we can tell where on the impedance trace a particular ECR isoperating during production. In the example given, the operatingfrequency of 41.552 kHz falls between the series resonance (f_(s)) andthe parallel resonance (f_(p)) points. This is normal operation. If theoperating frequency is outside of this range, the generator is mistunedand should be returned, or it is defective and should be replaced.

As mentioned above, with the test box 10 and method of the presentinvention, impedance traces may be generated for ECR transducer hornassemblies off-line under low and high power conditions. In addition,the test box 10 and method of the present invention allow for thegeneration of a variety of other electrical parameters on-line asdepicted in FIGS. 9 through 13. Interpretation of these traces allowsfor making judgments as to the operating condition of the ECR transducerhorn assemblies and as to the interaction of the THA with the otherassembly components of the ECR as well as to the efficiency of thedebubbling process. In particular, it is necessary to measure and setspecifications on the values of f_(s) (frequency at series resonance),f_(p) (frequency at parallel resonance), z_(s) (impedance at seriesresonance), and C_(o) (electrical capacitance) as determined from theimpedance traces. These specification values are based on efficiencyrequirements, the frequency operating range of the ECR generators beingused, cabling requirements, and also on direct measurements made on apopulation of good transducer horn assemblies. The specification valuesfor C_(o), f_(s), and f_(p) are dependent upon the tuning range of theparticular ECR generator being used. Any THA with a z_(s) which isgreater than 60 ohms should be removed from service. By comparing theimpedance traces generated with the test box 10 and method of thepresent invention, transducer horn assemblies which fall outside thelimits of the set specifications can be removed from service. It shouldbe recognized that the values of these parameters can be tracked overtime and through standard statistical techniques, trends in theseparameters can be used to set retesting and preventative maintenanceschedules for the transducer horn assemblies (THA).

The analysis of piezoelectric transducers and their use as sources ofultrasonic energy can be carried out by the application of the waveequation with appropriate boundary conditions and piezoelectricconstants. However, it is convenient and appropriate to use theequivalent circuit approach where both the electrical and mechanicalportions of the transducer are represented by electrical equivalents. Ifthe acoustic radiation takes place from one side, the transducer can berepresented by the electrical network shown in FIG. 14.

The electrical input to one side of the network, voltage (V) and current(I), result in the mechanical response, force (F) and particle motionalvelocity (u) at the output side. A mechanical system can be described byelectrical equivalent components. Using the analog between force andvoltage, and between velocity and current, the motional mass (M),motional stiffness (K), and radiation resistance (Zr), can be modeled byan inductance (Ls), a capacitance (Cs), and a resistance (R). With theuse of a conversion factor, N, that depends on the dimensions of thetransducer and the electromechanical coupling factor, the electricalcircuit diagram shown in FIG. 15 can be developed.

This circuit includes an ideal electromechanical transformer with turnsratio N between the electrical and mechanical sides of the transducer.The modeled mechanical components represented in the circuit as lumpedelements are actually continuously distributed throughout the THA. As aconsequence, the mechanical system can resonate at a series of higherharmonics whereas the electrical model of FIG. 14 resonates at only a"single harmonic". Since the THA is operated only in a single frequencyband, 38 kHz to 42 kHz, this model is used to represent the THA.

In general, it is a measure of how well a particular ECR can debubblethat is of interest. In other words, is the ECR operational, is it ingood condition or damaged, and if it is in working condition, howefficiently is it operating. With a measurement of the electricalimpedance made at the input of the transducer, information can bederived on the mechanical performance of the ECR. The model further aidsin understanding how well the TCAs work with different power suppliesand the potential benefits of working at parallel resonance as opposedto series resonance.

A procedure has been developed to measure the electrical impedance ofthe ECR horn. An impedance trace of a new ECR horn is shown in FIG. 16.The theoretical response curve for the equivalent circuit shown in FIG.15 is shown in FIG. 17.

By comparing FIGS. 16 and 17, values of the electrical circuit elementscan be derived. The electrical circuit with elements derived from a goodhorn can now be used for comparing the state of a given ECR horn andpredicting the operating efficiency.

From the equivalent circuit of FIG. 15 the equation for the inputimpedance can be derived as follows: ##EQU1## wherein C_(p) =staticcapacitance of the piezoelectric elements.

    ω=angular frequency(2πf)

    j=√-1;j.sup.2 =-1

Rearranging terms we get: ##EQU2##

The series resonance is defined as the frequency at which the term inthe numerator, ##EQU3## is zero. ##EQU4##

The impedance at f_(s) is a minimum. Substituting into Equation 2;##EQU5##

For a good THA, the value of jω_(s) C_(p) R is small compared to 1, andcan be neglected.

    Z.sub.s ≈R                                         (5)

The parallel resonance is defined as the frequency at which the term##EQU6## in the denominator of Equation 2 equals zero. ##EQU7##

The impedance at f_(p) is a maximum. Substituting into Equation 2;##EQU8##

For a good THA, ##EQU9## and, therefore, the impedance at parallelresonance becomes approximately, ##EQU10##

Note, that the impedances at both the series and parallel resonances foran unloaded THA are approximately real values. This can also be seenfrom the actual impedance trace of a horn in that the phase of theimpedance at f_(s) and f_(p) is zero indicating a real value ofimpedance.

For a transducer under liquid load, which is the normal operatingcondition of an ECR, the equivalent circuit can be modified to includeR_(loss) which represents losses within the horn and R_(load) withrepresents mechanical radiation. For completeness, a resistor, Rd,representing dielectric loss can also be added. The resulting equivalentcircuit is shown in FIG. 18, at series resonance, this reduces to thecircuit shown in FIG. 19. If the dielectric loss is assumed to benegligible (R_(d) →∞), the efficiency of the ECR horn can be determinedby; ##EQU11## where η is the efficiency and W_(load) and W_(loss) arethe power lost in the transducer and the radiated power respectively.The value R_(loss) can be determined for any individual horn from theseries resonance impedance, Equation 5. The determination is only validfor a good horn where the series resonant impedance occurs atapproximately zero phase angle. The value of R_(load) can also bedetermined from the impedance trace, in this case under loadedconditions. However, there is an interaction between the THA and the ECRhousing under liquid load and, therefore, this measurement is notroutinely made. A value of R_(load) has been determined for a good hornunder ideal conditions and this value is used in the efficiencycalculation. Based on Equation 9 and an assumed value of R=125 ohms fordistilled water, the calculated efficiency for an ECR THA can bedetermined using FIG. 20.

The overall power being delivered to the liquid for debubbling is thenthe product of the total input power, which is the wattmeter reading onthe front panel, and the efficiency of the THA. This assumes nocavitation and no effects from the geometry of the housing.

The electromechanical coupling factor, k_(c), is the ratio of the energystored mechanically to the energy stored electrically. It is defined as,##EQU12##

This value can be obtained from the frequency separation between f_(s)and f_(p), which represents the extremes in impedance or total current.Combining Equations 3 and 6 results in, ##EQU13##

The frequency separation, Δf=(f_(p) -f_(s)), is large for materials withhigh electromechanical coupling. C_(p) is the static capacitance of thecrystals that make up the THA. In our applications, there is also awiring capacitance that appears in parallel to C_(p) and effectivelycauses the measured values of C_(p) to be larger than the actual staticcapacitance. In general, the measurements of k_(c) include the wiringcapacitance which does not precisely fit the definition of k_(c) appliedto piezoelectric ceramics. However, it is useful for determiningproblems with wiring. The magnitude of this capacitance can effect thepower that is being delivered to the THA, either because of theincreased mismatch between the ECR and the generator which results inhigher required voltages or currents, or because it could shift theresonant frequency outside the tuning range of an autotune generator.Also, a large C_(p) means that Δf is small. It has been found that asmall Δf makes tuning of the generator more critical and more difficultto achieve.

The magnitude impedance of a good THA looks like that depicted in FIG.5. FIG. 7 shows the magnitude of the impedance of a badly damaged THAthat was removed from an actual manufacturing machine. The crystals werecracked in many places and chunks of ceramic had fallen off the crystal.In this case, the crystals are so damaged that the impedance tracecannot be analyzed according to the model. The electrical values f_(s),f_(p), Zs, Zp cannot be properly determined even though you can findmaximum and minimum values of impedance somewhere on the trace. Forextreme cases like this, the THA must be replaced.

There are basically two main ways the impedance trace shifts from theideal with changes in the electrical parameters of interest.

1) As R increases, Zs increases (by Equation 5) and Zp decreases (byEquation 8) but, f_(s) and f_(p) remain in about the same locationwithin the assumptions of the approximations. This shift is shown in themodeled responses of FIGS. 21 and 22 where R is low in FIG. 21 andincreases in FIG. 22. All other values remain the same.

2) As C_(p) increases, f_(s) remains the same, f_(p) decreases (byEquation 6) and Zp decreases (by Equation 8). Zs remains approximatelyconstant within the approximation of the assumption that ##EQU14## Thisshift is shown in the model response of FIGS. 21 and 23 where C_(p) islow in FIG. 21 and increases in FIG. 23. All other values remain thesame.

This yields some insight into the physical state of the ECR assembly asdescribed by its impedance trace.

A test was run to verify that there is a good correlation between thepredicted efficiency of an ECR as determined through the method andapparatus of the present invention and the measured capacity of the ECR.In this test, the flow rate of gelatin with 0.15% entrained air(bubbles) is increased until the ECR becomes overloaded and bubbles aredetected downstream from the ECR. This flow rate then becomes the y-axisvalue of the associated point plotted in FIG. 24. The test is run atdifferent viscosities resulting in different debubbling capacities for agiven THA. The efficiency calculations used different values of Rload toaccount for different loadings caused by the viscosity changes (Rload@40cp=150 Ω, Rload@130 cp=160 Ω). This experiment shows a good correlationbetween calculated horn efficiency and debubbling capacity.

From the foregoing it will be seen that this invention is one welladapted to attain all of the ends and objects hereinabove set forthtogether with other advantages which are apparent and which are inherentto the process.

It will be understood that certain features and subcombinations are ofutility and may be employed with a reference to other features andsubcombinations. This is contemplated by and is within the scope of theclaims.

As many possible embodiments may be made of the invention withoutdeparting from the scope thereof, it is to be understood that all matterherein set forth and shown in the accompanying drawings is to beinterpreted as illustrative and not in a limiting sense.

What is claimed is:
 1. A method for evaluating the performance of atransducer horn assembly used in a debubbling operation, the methodcomprising the steps of:(a) connecting a test circuit between thetransducer horn assembly and a signal analyzer; (b) operating thetransducer horn assembly off-line and generating a frequency dependentimpedance trace for the transducer horn assembly; (c) operating thetransducer horn assembly on-line in a debubbling operation; (d) samplingelectrical signals applied to the transducer horn assembly during theoperating step (c); (e) transmitting the sampled electrical signals tothe signal analyzer; (f) maintaining the amplitude and phaserelationship of the sampled electrical signals; (g) determining theoperating frequency of the transducer horn assembly from the sampledelectrical signals; and (h) determining if the operating frequency ofthe transducer horn assembly is between a series resonance frequency anda parallel resonance frequency of the transducer horn assembly accordingto the off-line generated frequency dependent impedance trace of step(b).